Lot Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation

Authors:
Alper Atamtürk;Simge Küçükyavuz
Affiliations:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720-1777;Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720-1777
Venue:
Operations Research
Year:
2005

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Abstract

We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one with linear cost on inventory, the other with linear and fixed costs on inventory. For both models, we identify facet-defining inequalities that make use of the inventory bounds explicitly and give exact separation algorithms. We also describe a linear programming formulation of the problem when the order and inventory costs satisfy the Wagner-Whitin nonspeculative property. We present computational experiments that show the effectiveness of the results in tightening the linear programming relaxations of the lot-sizing problem with inventory bounds and fixed costs.